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Math 104: Homework 3-
1. Let (an) be a sequence defined according to a1 = t where t > 0, and an+1 = 2an/(1+an) for n ∈ N. Prove that an → 1 as n → ∞.
2. Let (sn) and (tn) be Cauchy sequences defined on R, and let (un) be a sequence defined as un = asn + btn for all n, where a, b ∈ R. By using the definition of a Cauchy sequence only, without assuming that limits of (sn) and (tn) exist, prove that (un) is a Cauchy sequence.
3. Let (sn) be a sequence defined by sn = (-1)n(1 + 1/n). Prove that lim sup sn = 1 and lim infsn = -1.
You have just graduated from college, and you have started your first big project at your new job. Your boss informs you that you are responsible for the Equations and Inequalities section of the project and for presenting your ideas to the team.
a baseball diamond is a square 90 feet on each side. a player is running from home to first base at a rate of 15 feet per second. at what rate is his distance from second base changing when he has run halfway to first base?
Find the Fourier Transform of f(x) = e^((-x^2)/(2a^2). note: complete the square in the x term in the exponent and make the change of variable; y=x+(*a^2)*i*b.
The length of a rectangle is 1 cm longer than its width. If the diagonal of the rectangle is 4 cm, what are the dimensions (the length and the width) of the rectangle?
A poster is to have an area of 240 in2 with 1 inch margins at the bottom and sides and a 7 inch margin at the top. What dimensions will give the largest printed area? (Give your answers correct to one decimal place.)
Assume that for each type of system below there is at least one variable with a nonzero coefficient. Find the smallest and largest rank possible for the corresponding augmented matrix in each case.
1. Wang Distributors has an annual demand for an airport metal detector of 1,400 units. The cost of a typical detector to Wang is $400. Carrying cost is estimated to be 20% of the unit cost, and the ordering cost is $25 per order. If Ping Wang, t..
use vector techniques to prove that a triangle and its medial triangle have the same centroid stating each step of the
Find the critical points.
Find the total charge on the disk.
Find the interval of convergence for the following series
Draw a tree diagram that illustrates the following. Three-fifths of kindergarten children are bussed to school, while two-fifths of the first to fifth graders are bussed.
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